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Stochastic models for protein production : the impact of autoregulation, cell cycle and protein production interactions on gene expression

Abstract : The mechanism of protein production, to which is dedicated the majority of resources of the bacteria, is highly stochastic: every biochemical reaction that is involved in this process is due to random collisions between molecules, potentially present in low quantities. The good understanding of gene expression requires therefore to resort to stochastic models that are able to characterise the different origins of protein production variability as well as the biological devices that potentially control it.In this context, we have analysed the variability of a protein produced with a negative autoregulation mechanism: i.e. in the case where the protein is a repressor of its own gene. The goal is to clarify the effect of this feedback on the variance of the number of produced proteins. With the same average protein production, we sought to compare the equilibrium variance of a protein produced with the autoregulation mechanism and the one produced in “open loop”. By studying the model under a scaling regime, we have been able to perform such comparison analytically. It appears that the autoregulation indeed reduces the variance; but it is nonetheless limited: an asymptotic result shows that the variance won't be reduced by more than 50%. The effect on the variance being moderate, we have searched for another possible effect for autoregulation: it havs been observed that the convergence to equilibrium is quicker in the case of a model with autoregulation.Classical models of protein production usually consider a constant volume, without any division or gene replication and with constant concentrations of RNA-polymerases and ribosomes. Yet, it has been suggested in the literature that the variations of these quantities during the cell cycle may participate to protein variability. We propose a series of models of increasing complexity that aims to reach a realistic representation of gene expression. In a model with a changing volume that follows the cell cycle, we integrate successively the protein production mechanism (transcription and translation), the random segregation of compounds at division, and the gene replication. The last model integrates then all the genes of the cell and takes into account their interactions in the productions of different proteins through a common sharing of RNA-polymerases and ribosomes, available in limited quantities. For the models for which it was possible, the mean and the variance of the concentration of each proteins have been analytically determined using the Marked Poisson Point Processes. In the more complex cases, we have estimated the variance using computational simulations. It appears that, among all the studied mechanisms, the main source of variability comes from the protein production mechanism itself (referred as “intrinsic noise”). Then, among the other “extrinsic” aspects, only the random segregation of compounds at division seems to have potentially a significant impact on the variance; the other aspects show only a limited effect on protein concentration. These results have been confronted to some experimental measures, and show a still unexplained decay between the theoretical predictions and the biological data; it instigates the formulations of new hypotheses for other possible sources of variability.To conclude, the processes studied have allowed a better understanding of biological phenomena by exploring some hypotheses that are difficult to test experimentally. In the studied models, we have been able to indicate theoretically some trends; hence showing that the stochastic modelling is an important tool for a good understanding of gene expression mechanisms.
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Renaud Dessalles. Stochastic models for protein production : the impact of autoregulation, cell cycle and protein production interactions on gene expression. Probability [math.PR]. Université Paris Saclay (COmUE), 2017. English. ⟨NNT : 2017SACLX005⟩. ⟨tel-01509431⟩

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